Let $M$ be a nondoubling parabolic manifold with ends. In this study, we will investigate the $L^p$ boundedness of the discrete square function in terms of the Littlewood-Paley decomposition. It should be pointed out that, in our setting, the doubling condition of the underlying space and the regularity estimate of the kernel are missing.
The authors would like to thank the anonymous referees for their helpful and constructive comments that greatly contributed to improving the final version of the paper. The author would like to thank X. T. Duong and T. A. Bui for helpful advice and discussion.
"Boundedness of the Discrete Square Function on Nondoubling Parabolic Manifolds with Ends." Taiwanese J. Math. 25 (2) 303 - 331, April, 2021. https://doi.org/10.11650/tjm/201001